When you have converted a mesh and the mesh is ok (check it with checkMesh . <case_name> in OpenFOAM-1.4.1, or just checkMesh in the case file in OpenFOAM-1.5) you should not need to build the mesh with blockMesh. Have a go at checkMesh and then just run the case, it should work.

As you probably have found the setup of an OpenFOAM case there are three folders: "system", "0", and "constant". If you convert your mesh using fluentMeshToFoam (not fluentMeshToOpenFoam) the appropriate files /constant/polyMesh/ describing your case in OpenFOAM format. It is easiest to use a tutorial which best fits the case you want to run and then adjust the files.The thing is then that you still need to adjust the initial and boundary conditions in "0" and "constant" so that the initial conditions make sense to your case and that things like the walls and inlets-outlets have the same name as described in your converted polyMesh file. If you have different names the case will not solve and you can't even view the case properly in ParaView.